The use of energy constraints within filtering and smoothing

This paper considers estimation problems where the energy of a linear system´s output is constrained. A low-cost filtering procedure is proposed in which the input measurements are constrained by nonlinear censuring functions. A similar smoothing procedure for off-line applications is also described. It is shown that the filtered and smoothed output estimates satisfy a performance bound. It is also established that the resulting estimates are unbiased, and the estimation errors are bounded.